Problem 6 · 2004 AMC 8
Easy
Fractions, Decimals & Percents
percent-equation
After Sally takes 20 shots, she has made 55% of her shots. After she takes 5 more shots, she raises her percentage to 56%. How many of the last 5 shots did she make?
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Answer: C — 3.
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Hint 1 of 2
Percentages are slippery, but made shots are whole numbers. Convert each percentage into an actual count of baskets — then the answer is just the difference between the two counts.
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Hint 2 of 2
The technique is turn rates into counts: a percent of a known total is a concrete number you can subtract. Don't manipulate the percents; manipulate the makes.
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Approach: convert percents to make-counts, then subtract
- Before: 55% of 20 = 11 made. After: 56% of 25 = 14 made. Both must be whole numbers — baskets don't come in fractions — which is the quiet reason the percents were chosen to land cleanly.
- The last 5 shots added 14 − 11 = 3 made baskets.
- Sanity check: she made 3 of 5 new shots (60%), which is higher than her old 55% — consistent with her average creeping up to 56%.
Another way — solve for the unknown makes:
- Let x be the new makes. Then (11 + x) / 25 = 0.56.
- So 11 + x = 14, giving x = 3.
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